In this paper, we employ the generalized prolate spheroidal wave function, generalized hypergeometric function, general class of polynomials and the I-function in obtaining the formal solution of a partial differential equation related to a problem of heat conduction in an anisotropic material. This type of problem occurs mainly in wood technology, soil mechanics and the mechanics of solids of fibrous structure. At the end, we give an application of our main finding by inner-connecting them with the Riemann- Liouville type of functional integral operator. The results of this paper unify and extend a large number of results established by various earlier workers.